Problem: Solve for $x$ and $y$ using elimination. ${3x+y = 33}$ ${-2x-y = -23}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {3x+y = 33}\thinspace$ to find $y$ ${3}{(10)}{ + y = 33}$ $30+y = 33$ $30{-30} + y = 33{-30}$ ${y = 3}$ You can also plug ${x = 10}$ into $\thinspace {-2x-y = -23}\thinspace$ and get the same answer for $y$ : ${-2}{(10)}{ - y = -23}$ ${y = 3}$